Planar solutions of higher-spin theory. Nonlinear corrections

Abstract

Leading order higher-spin corrections to the linearized higher-spin black brane are analyzed in four dimensions. It is shown that the static solution that respects planar symmetry exists in the bosonic case at given order. Its higher-spin Weyl tensors are found in a closed form and are shown to have the double copy origin. The effect of higher-spin fields to form a strictly positive scalar condensate for any values of higher-spin charges is observed.

Metaplectic representation and ordering (in)dependence in Vasiliev’s higher spin gravity

“…We shall consider expansions of the local data on SpH(4, C) group elements, where SpH(4, C) is defined as the semi-direct product of Sp(4, C) and the 4-dimensional Heisenberg group: that is, exponentials of inhomogeneous quadratic polynomials in oscillators Y α = ( y α , ȳ α) satisfying a Heisenberg algebra, with complex coefficients. One of the motivations to do so is that specific Gaussian projectors have been found (in Weyl ordering) to encode some of the most relevant field configurations, appearing as solutions to either the full field equations or the linearized ones around (A)dS: among these are massless particle states [20,22,33], bulk-to-boundary propagators [29,34,35], black-hole and black-brane-like solutions [19][20][21][22][35][36][37][38][39], instantons, domain walls and FLRW-like solutions [23,40,41]. In the case of scalar particle and black hole states, we shall show that such projectors are given by evanescent pieces of Sp(4, C) group algebra elements in singular limits.…”